Question 1

Given   ,   , and   , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Find the product   using trigonometric forms. Leave the result in trigonometric form.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Given   and   , determine   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

Find the absolute value of the complex number   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Find the standard form of the complex number   . Round values to the nearest hundredth.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

In the figure below,   ,   , and   . Use this information to solve the parallelogram for b. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Accepted Answer

A)  6.33 
B)  5.91 
C)  9.27 
D)  7.59 
E)  2.54 
A)  6.33 
B)  5.91 
C)  9.27 
D)  7.59 
E)  2.54

Question 7

Given   , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)  not possible 
A)    
B)    
C)    
D)    
E)  not possible

Question 8

Given   ,   , and   , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]

Accepted Answer

A)    
B)    
C)    
D)  none of these 
E)    
A)    
B)    
C)    
D)  none of these 
E)

Question 10

Use DeMoivre's Theorem to find the indicated power of the following complex number.

Accepted Answer

A)  -324 
B)  729 
C)  324 
D)  2,916 
E)  243 
A)  -324 
B)  729 
C)  324 
D)  2,916 
E)  243

Question 11

Given   ,   , and   , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Given   ,   , and   , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Let w be a vector with initial point   and terminal point   . Write w as a linear combination of the standard unit vectors i and j.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Find the magnitude of vector v.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Find the component form of v if   and the angle it makes with the x-axis is   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

The vector   gives the number of units of two models of laptops produced by a company. The vector   gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 6%.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Find the magnitude of vector v with initial point   and terminal point   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

In the figure below,   ,   , and   . Use this information to solve the parallelogram for c. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Accepted Answer

A)  10.00 
B)  7.21 
C)  10.93 
D)    
E)  12.17 
A)  10.00 
B)  7.21 
C)  10.93 
D)    
E)  12.17

Question 19

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]

Accepted Answer

A)    
B)    
C)    
D)  none of these 
E)    
A)    
B)    
C)    
D)  none of these 
E)

Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Find the product using trigonometric forms. Leave the result in trigonometric form.

Given and , determine .

Find the absolute value of the complex number .

Find the standard form of the complex number . Round values to the nearest hundredth.

In the figure below, , , and . Use this information to solve the parallelogram for b. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Given , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.

Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]

Use DeMoivre's Theorem to find the indicated power of the following complex number.

Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.

Given , , and , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Let w be a vector with initial point and terminal point . Write w as a linear combination of the standard unit vectors i and j.

Find the magnitude of vector v.

Find the component form of v if and the angle it makes with the x-axis is .

The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 6%.

Find the magnitude of vector v with initial point and terminal point .

In the figure below, , , and . Use this information to solve the parallelogram for c. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Prerequisites

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Exam 7: Additional Topics in Trigonometry

Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Find the product using trigonometric forms. Leave the result in trigonometric form.

Given and , determine .

Find the absolute value of the complex number .

Find the standard form of the complex number . Round values to the nearest hundredth.

In the figure below, , , and . Use this information to solve the parallelogram for b. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Given , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.

Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]

Use DeMoivre's Theorem to find the indicated power of the following complex number.

Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.

Given , , and , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Let w be a vector with initial point and terminal point . Write w as a linear combination of the standard unit vectors i and j.

Find the magnitude of vector v.

Find the component form of v if and the angle it makes with the x-axis is .

The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 6%.

Find the magnitude of vector v with initial point and terminal point .

In the figure below, , , and . Use this information to solve the parallelogram for c. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Prerequisites

Filters